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What you always wanted to know about Datalog (and never dared to ask)
 IEEE TRANSACTIONS KNOWLEDGE AND DATA ENGINEERING
, 1989
"... Datalog is a database query language based on the logic programming paradigm; it has been designed and intensively studied over the last five years. We present the syntax and semantics of Datalog and its use for querying a relational database. Then, we classify optimization methods for achieving eff ..."
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Datalog is a database query language based on the logic programming paradigm; it has been designed and intensively studied over the last five years. We present the syntax and semantics of Datalog and its use for querying a relational database. Then, we classify optimization methods for achieving efficient evaluations of Datalog queries, and present the most relevant methods. Finally, we discuss various exhancements of Datalog, currently under study, and indicate what is still needed in order to extend Datalog’s applicability to the solution of reallife problems. The aim of this paper is to provide a survey of research performed on Datalog, also addressed to those members of the database community who are not too familiar with logic programming concepts.
Physics and Leibniz’s Principles
 Symmetries in Physics: Philosophical Reflections
"... Leibnizs principles made for an elegant and coherent philosophy. In part metaphysical, in part methodological, they addressed fundamental questions in the treatment of symmetry, in the relationship of physics to mathematics, in logicthat are if anything even more pressing today than they were in ..."
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Leibnizs principles made for an elegant and coherent philosophy. In part metaphysical, in part methodological, they addressed fundamental questions in the treatment of symmetry, in the relationship of physics to mathematics, in logicthat are if anything even more pressing today than they were in Leibnizs time. As I shall read them, they also expressed a distinctive and uncompromising form of realism, a commitment to the adequacy of purely descriptive concepts. This doctrine has been called semantic universalismby van Fraassen (1991), and the generalist pictureby OLearyHawthorne and Cover (1996): it will become clearer in due course just what it entails. The principles that I shall consider are the Principle of Su ¢ cient Reason (PSR) and the Principle of Identity of Indiscernibles (PII). In the
rst instance I shall take them both to be methodological principles. The former I shall read as requiring that the concepts of physics be entirely transparent. Analysis and explanation are to proceed without any limits. The perspective is impersonal: any epistemological limitation, to do with our human situation or perceptual ap
Hilbert’s twentyfourth problem
 American Mathematical Monthly
, 2001
"... 1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Cong ..."
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1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of
Nonmonotonic Reasoning
 In Proc
, 1993
"... Classical logic is the study of ”safe ” formal reasoning. Western Philosophers developed classical logic over a period of thirtythree centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and B ..."
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Classical logic is the study of ”safe ” formal reasoning. Western Philosophers developed classical logic over a period of thirtythree centuries after its introduction in the form of syllogistic by Aristotle [1] in the third century B. C. Beginning in the nineteenth century with De Morgan [2] and Boole [3], responsibility for the development of classical logic moved from the philosophical to the mathematical community.
The Semantics of Jitter in Anticipating Time Itself within NanoTechnology
"... Abstract. The development of nanotechnology calls for a careful examination of anticipatory systems at this small scale. For the characteristics of time at the boundary between classical and quantum domains are quite critical for the advancement of the new technology. It has long been well recognis ..."
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Abstract. The development of nanotechnology calls for a careful examination of anticipatory systems at this small scale. For the characteristics of time at the boundary between classical and quantum domains are quite critical for the advancement of the new technology. It has long been well recognised that time is not absolute even in classical subjects like navigation and dynamics where idealised concepts like mean solar time, International Atomic Time and Newton’s dynamical time have had to be used. Time is the data of the Universe and belongs in the semantics of its extensional form. At the boundary between classical and quantum behaviour the uncertainty of time data becomes a significant effect and this is why it is of great importance in nanotechnology, in areas such as the interoperability of different time domains in hardware, where noise in the form of jitter causes a system to behave in an unpredictable fashion, a severe and expensive problem for anticipating how time is to be handled. A fundamental difficulty is that jitter is represented using numbers, giving rise to undecidability and incompleteness according to Gödel’s theorems. To escape the clutches of Gödel undecidability it is necessary to advance to cartesian closed categories beyond the category of sets to represent the relationship between different times as adjoint endofunctors in monad and comonad constructions.
On a Straw Man in the Philosophy of Science —A Defense of the Received View—
"... I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must in ..."
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I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories.
The Gödel completeness theorem for uncountable languages
 Formalized Mathematics
"... Summary. This article is the second in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [15] for uncountably large languages. We follow the proof given in [16]. The present article contains the techniques required to expand a theory such that the expande ..."
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Summary. This article is the second in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [15] for uncountably large languages. We follow the proof given in [16]. The present article contains the techniques required to expand a theory such that the expanded theory contains witnesses and is negation faithful. Then the completeness theorem follows immediately.
Proving FirstOrder Equality Theorems with HyperLinking
, 1995
"... Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving p ..."
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Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving problems. However, Lee's roundbyround implementation of hyperlinking is not particularly well suited for the addition of special methods in support of equality. In this dissertation, we describe, as alternative to the roundbyround hyperlinking implementation of Lee, a smallest instance first implementation of hyperlinking which addresses many of the inefficiencies of roundbyround hyperlinking encountered when adding special methods in support of equality. Smallest instance first hyperlinking is based on the formalization of generating smallest clauses first, a heuristic widely used in other automated theorem provers. We prove both the soundness and logical completeness of smallest instance first hyperlinking and show that it always generates smallest clauses first under